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Algebra II with Trig Ch8.3 #26

Question from Elisha:

I just took the Trig. Final Test for your Alg. 2/ Trig. Course.  My mom and I were checking it and on problem 26 from section 8.3, my answer is different from the one you give in the answers.  I see that you add 45 degrees to the 25-degree angle and I didn’t.  I’m not sure exactly why that is and what I did wrong.  I have attached a photocopy of my work.  Could you tell me if my answer is wrong and if so why? Thanks for your help.  I have really enjoyed the course. J Elisha

Answer from Dr. Callahan: 

You are missing one key thing…the angle between 15mph and 3.9 mph is not 25 degrees.

The angle between due north and the direction is 25degrees. The angle between the direction of the boat and the direction of the water should be 70degrees. See example 1 again.

Here is the solution worked out in a drawing. A2T Ch8.3#26